Embeddings of an M12 Geometry: Some Simple Combinatorial Descriptions
نویسندگان
چکیده
منابع مشابه
A combinatorial construction of an M12-invariant code
A ternary [66, 10, 36]3-code admitting the Mathieu group M12 as a group of automorphisms has recently been constructed by N. Pace, see [2]. We give a construction of the Pace code in terms of M12 as well as a combinatorial description in terms of the small Witt design, the Steiner system S(5, 6, 12). We also present a proof that the Pace code does indeed have minimum distance 36.
متن کاملSome Constructions and Embeddings of the Tilde Geometry
Some old and new constructions of the tilde geometry (the flag transitive connected triple cover of the unique generalized quadrangle W(2) of order (2, 2)) are discussed. Using them, we prove some properties of that geometry. In particular, we compute its generating rank, we give an explicit description of its universal projective embedding and we determine its homogeneous embeddings.
متن کاملCombinatorial Embeddings of Manifolds
The following results on embedding manifolds resemble in their form Dehn's Lemma, the Sphere Theorem, and, especially, embedding theorems obtained for differentiable manifolds by A. Haefliger [i]. Let M, Q be finite combinatorial manifolds of dimensions m and q, respectively. Let M, Q be their boundaries (possibly empty), and let ƒ : M—>Q be a piecewise linear map. We define sing (ƒ) to be the ...
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملOn the Computational Complexity of some problems from Combinatorial Geometry
We study several canonical decision problems that arise from the most famous theorems from combinatorial geometry. We show that these are W[1]-hard (and NP-hard) if the dimension is part of the input by fpt-reductions (which are actually ptime-reductions) from the d-Sum problem. Among others, we show that computing the minimum size of a Caratheodory set and a Helly set and certain decision vers...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1988
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(88)80045-3